Which of the following functions have graphs that reflect their respective parent functions over the x-axis? Select all that apply.
a. g(x) = -2^x
b. g(x) = (-2)^x
c. g(x) = 4th root(-3x)
d. g(x) = -1/3 4th root(x)
e. g(x) = - absolute value(x)
f. g(x) = absolute value(-5x)
A) g(x)= -2^x
D) g(x)= -1/3 4th root x
E) g(x)= -|x|
Just find the reciprocal of the parent function :)
Parent functions:
g(x)= (1/2)^x
g(x)= 4 cube root x
g(x)= |x|
Goodluck!!
Answers are
A
D
E
You suck steve.
desiree is right !<3
To determine if a function reflects its parent function over the x-axis, we need to check if changing the sign of the function affects its graph. The parent functions we will consider are f(x) = x and f(x) = |x|.
a. g(x) = -2^x
To check if the graph of g(x) reflects the parent function f(x) = x over the x-axis, we can evaluate g(x) at a point x, and then evaluate -g(x) at the same point x. If the values are the same, then the graph is reflected over the x-axis.
Let's find g(0):
g(0) = -2^0 = -1
Now let's find -g(0):
-g(0) = -(-1) = 1
Since g(0) is not equal to -g(0), the graph of g(x) = -2^x does not reflect the parent function f(x) = x over the x-axis.
b. g(x) = (-2)^x
To check if the graph of g(x) reflects the parent function f(x) = x over the x-axis, we can again evaluate g(x) at a point x, and then evaluate -g(x) at the same point x.
Let's find g(0):
g(0) = (-2)^0 = 1
Now let's find -g(0):
-g(0) = -(1) = -1
Since g(0) is equal to -g(0), the graph of g(x) = (-2)^x reflects the parent function f(x) = x over the x-axis.
c. g(x) = 4th root(-3x)
To check if the graph of g(x) reflects the parent function f(x) = x over the x-axis, we need to evaluate g(x) and -g(x) at a point x.
There is no specific point provided, so let's choose x = 1:
g(1) = 4th root(-3(1)) = 4th root(-3) ≈ -1.316
Now let's find -g(1):
-g(1) = -(4th root(-3)) ≈ 1.316
Since g(1) is not equal to -g(1), the graph of g(x) = 4th root(-3x) does not reflect the parent function f(x) = x over the x-axis.
d. g(x) = -1/3 4th root(x)
To check if the graph of g(x) reflects the parent function f(x) = x over the x-axis, we need to evaluate g(x) and -g(x) at a point x.
Again, there is no specific point provided, so let's choose x = 1:
g(1) = -1/3 4th root(1) = -1/3
Now let's find -g(1):
-g(1) = -(-1/3) = 1/3
Since g(1) is equal to -g(1), the graph of g(x) = -1/3 4th root(x) reflects the parent function f(x) = x over the x-axis.
e. g(x) = - absolute value(x)
The graph of g(x) = -|x| is the reflection of the parent function f(x) = |x| over the x-axis. So, the graph of g(x) reflects the parent function f(x) = x over the x-axis.
f. g(x) = absolute value(-5x)
The graph of g(x) = |(-5x)| is the reflection of the parent function f(x) = |x| over the x-axis. So, the graph of g(x) reflects the parent function f(x) = x over the x-axis.
Therefore, the functions that have graphs reflecting their respective parent functions over the x-axis are:
b. g(x) = (-2)^x
e. g(x) = - absolute value(x)
f. g(x) = absolute value(-5x)
a. g(x) = -2^x
d. g(x)= -1/3 4th root (x)
f. g(x)= |-5x|
reflection over the x-axis takes (x,y) -> (x,-y)
so, what do you think?